This summer, I will be having meetings with my Ph.D. advisor, and since he's traveling, we'll be meeting via Skype or FaceTime. Since we are working on mathematics, we need a way to see each other's writing, so we can quickly suggest ideas to each other and talk about them.

He will be using a MacBook Pro 2017 and I'll be using my iMac 2018 or MacBook Pro 2017.
I have an iPad pro with Apple Pencil; I'm not sure if he does. I mention this because it may be a solution that we have separate writing apps open on our iPads even as we FaceTime. In case he doesn't have an iPad already, he will of course need to get some device that has the ability to receive handwriting.